Electrophoretic traveling waves
Authors:
P. C. Fife, O. A. Palusinski and Y. Su
Journal:
Trans. Amer. Math. Soc. 310 (1988), 759780
MSC:
Primary 35Q20; Secondary 76R99, 92A40
MathSciNet review:
973176
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Abstract 
References 
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Additional Information
Abstract: An existenceuniquenessapproximability theory is given for a prototypical mathematical model for the separation of ions in solution by an imposed electric field. The separation is accomplished during the formation of a traveling wave, and the mathematical problem consists in finding a traveling wave solution of a set of diffusionadvection equations coupled to a Poisson equation. A basic small parameter appears in an apparently singular manner, in that when (which amounts to assuming the solution is everywhere electrically neutral), the last (Poisson) equation loses its derivative, and becomes an algebraic relation among the concentrations. Since this relation does not involve the function whose derivative is lost, the type of "singular" perturbation represented here is nonstandard. Nevertheless, the traveling wave solution depends in a regular manner on , even at ; and one of the principal aims of the paper is to show this regular dependence.
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McGrawHill Book Company, Inc., New YorkTorontoLondon, 1955. MR 0069338
(16,1022b)
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Z. Deyl, ed., Electrophoresis: A survey of techniques and applications, Elsevier, Amsterdam, 1979.
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V. P. Dole, A theory of moving boundary systems formed by strong electrolytes, J. Amer. Chem. Soc. 67 (1945), 119.
 [K]
F. Kohlrausch, Ueber ConcentrationsVerschiebungen durch Electrolyse im Inneren von Losungen und Losungsgemischen, Ann. Physik 62 (1897), 209.
 [SP]
D. A. Saville and O. A. Palusinski, Theory of electrophoretic separations, Parts 1 and 2, AIChE J. 32 (1986).
 [Ag]
 D. Agin, Electroneutrality and electrodiffusion in the squid axon, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 12321238.
 [Al]
 R. A. Alberty, Moving boundary systems formed by weak electrolytes: Theory of simple systems formed by weak acids and bases, J. Amer. Chem. Soc. 72 (1950), 361.
 [ABR]
 R. A. Arandt, J. D. Bond, and L. D. Roper, Electrical approximate solutions of steadystate electrodiffusion for a simple membrane, J. Theoret. Biol. 34 (1972), 265276.
 [B]
 M. Bier et al., Electrophoresis: Mathematical modeling and computer simulation, Science 219 (1983), 281.
 [CB]
 M. Coxon and M. J. Binder, Isotachophoresis theory, J. Chromatogr. 95 (1974), 133.
 [CL]
 E. Coddington and N. Levinson, Theory of ordinary differential equations, McGrawHill, New York, 1955. MR 0069338 (16:1022b)
 [De]
 Z. Deyl, ed., Electrophoresis: A survey of techniques and applications, Elsevier, Amsterdam, 1979.
 [Do]
 V. P. Dole, A theory of moving boundary systems formed by strong electrolytes, J. Amer. Chem. Soc. 67 (1945), 119.
 [K]
 F. Kohlrausch, Ueber ConcentrationsVerschiebungen durch Electrolyse im Inneren von Losungen und Losungsgemischen, Ann. Physik 62 (1897), 209.
 [SP]
 D. A. Saville and O. A. Palusinski, Theory of electrophoretic separations, Parts 1 and 2, AIChE J. 32 (1986).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198809731764
PII:
S 00029947(1988)09731764
Keywords:
Electrophoresis,
traveling waves,
singular perturbation,
diffusionadvection equations,
Schauder fixed points
Article copyright:
© Copyright 1988
American Mathematical Society
